$\text{a)}\text{tg}\alpha =5\Rightarrow \frac{\sin \alpha }{\cos \alpha }=5\Rightarrow \sin \alpha =5\cos \alpha$  

$\frac{4\sin \alpha -5\cos \alpha }{\cos \alpha +3\sin \alpha }=\frac{4\cdot 5\cos \alpha -5\cos \alpha }{\cos \alpha +3\cdot 5\cos \alpha }=\frac{3\cdot 5\cos \alpha }{\cos \alpha +15\cos \alpha }=\frac{15\cos \alpha }{16\cos \alpha }=\frac{15}{16}$  

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$\text{b)}\text{ctg}\alpha =-2\Rightarrow \frac{\cos \alpha }{\sin \alpha }=-2\Rightarrow \cos \alpha =-2\sin \alpha$  

$\frac{-3\cos \alpha +6\sin \alpha }{8\sin \alpha +3\cos \alpha }=\frac{-3\cdot \left(-2\sin \alpha \right)+6\sin \alpha }{8\sin \alpha +3\cdot \left(-2\sin \alpha \right)}=\frac{6\sin \alpha +6\sin \alpha }{8\sin \alpha -6\sin \alpha }=\frac{12\sin \alpha }{2\sin \alpha }=6$